“We have deep depth” is a jocular redundancy that a sports manager or coach says about his or her well-stocked team. Baltimore Orioles manager Earl Weaver (1930-2013)  was credite with “We have deep depth” in July 1979.
 
Yogi Berra (1925-2015), who managed both the New York Yankees and New York Mets, is frequently credited with the line, but Weaver originated it.
 
   
Wikipedia: Earl Weaver
Earl Sidney Weaver (August 14, 1930 – January 19, 2013) was an American professional baseball player, Hall of Fame Major League manager, author, and television broadcaster. After playing in minor league baseball, he retired without playing in Major League Baseball (MLB). He became a minor league manager, and then managed in MLB for 17 years with the Baltimore Orioles (1968–82; 1985–86). Weaver’s style of managing was summed up in the quote: “pitching, defense, and the three-run homer.” He did not believe in placing emphasis on “small ball” tactics such as stolen bases, hit and run plays, or sacrifice bunts. He was inducted into the Baseball Hall of Fame in 1996.
     
15 July 1979, Seattle (WA) Times, “Despite injuries, Weaver’s Orioles flying high” by Hy Zimmerman, pg. C3, col. 3:
So how, in the midst of misery, did the Orioles remain on the wing? Earl, resorting to what have become tabbed as Weaverisms, responded: “We have deep depth.”
 
16 July 1979, Washington (DC) Star, “Orioles End Trip With 6-2 Victory” by Dan Shaughnessy, pg. D-1, col. 6:
“We still have deep depth, gentleman,” Weaver said.
 
24 July 1979, The Evening Sun (Hanover, PA), “Birds Club A’s,” pg. D-5, col. 7:
BALTIMORE (AP)—“It’s great to have that deep depth,” Earl Weaver said, chortling his oft-repeated description of the Baltimore Orioles which offers more truth than redundancy.
 
9 June 1988, Cedar Rapids (IA) Gazette, “Pistons,” pg. 2C, col. 1:
The Pistons, to steal a Yogi Berra line, have deep depth.
 
Google Books
When You Come to a Fork in the Road, Take It!:
Inspiration and Wisdom from One of Baseball’s Greatest Heroes
By Yogi Berra with Dave Kaplan
New York, NY: Hyperion
2001
Pg. ?:
WE HAVE DEEP DEPTH
 
Google Books
Baseball’s Greatest Quotations (Rev. Ed.):
An Illustrated Treasury of Baseball Quotations and Historical Lore
By Paul Dickson
New York, NY: Collins
2008
Pg. 58 (BERRAISMS/YOGISMS):
“We have deep depth.”
—SABR Collector
 
Orioles.com
05/02/12 8:34 PM ET
Endy knows his role, and does it well
By Marty Noble / MLB.com
(...)
The Yankees will have “deep depth” as Earl Weaver used to say.
 
ForTheWin
The 50 greatest Yogi Berra quotes
By: Nate Scott | September 23, 2015 7:30 am
(...)
21. We have deep depth.